MAXIMIZATION OF PRODUCTION AND NET INCOME IN AGRO-FOREST SYSTEMS

Nascimento, Vinicius T. do; Ventura, Sergio D.; Delgado, Angel R. S.; Silva, Washington S. da

doi:10.1590/1809-4430-Eng.Agric.v42n2e20210017/2022

Vinicius T. do Nascimento ^** Corresponding author. Universidade Federal Rural do Rio de Janeiro - UFRRJ/ Seropédica - RJ, Brasil. E-mail: vinicius.nascimento@ufrrj.br

Universidade Federal Rural do Rio de Janeiro - UFRRJ/ Seropédica - RJ, Brasil.

http://orcid.org/0000-0003-0070-4086

Sergio D. Ventura

Universidade Federal Rural do Rio de Janeiro - UFRRJ/ Seropédica - RJ, Brasil.

Angel R. S. Delgado

Universidade Federal Rural do Rio de Janeiro - UFRRJ/ Seropédica - RJ, Brasil.

Washington S. da Silva

Universidade Federal Rural do Rio de Janeiro - UFRRJ/ Seropédica - RJ, Brasil.

* Corresponding author. Universidade Federal Rural do Rio de Janeiro - UFRRJ/ Seropédica - RJ, Brasil. E-mail: vinicius.nascimento@ufrrj.br

Area Editor: Danilton Luiz Flumignan

PLANT	PRODUCTION FUNCTION ( kg.ha ⁻¹)
1	$y_{1} (r, w, n) = - 9.47 \cdot 10^{5} r^{2} - 4.52 \cdot 10^{- 5} w^{2} - 4.27 \cdot 10^{- 5} n^{2} + 4, 943.42 r + 0.0257349 w + 0.0317876 n + 0.1225433 r$
2	$y_{2} (r, w, n) = - 5.07 \cdot 10^{5} r^{2} - 8.50 \cdot 10^{- 5} w^{2} - 5.94 \cdot 10^{- 5} n^{2} + 73, 350.85 r + 0.0335390 w + 0.0157880 n + 4.3457454$
3	$y_{3} (r, w, n) = - 6.99 \cdot 10^{5} r^{2} - 8.15 \cdot 10^{- 5} w^{2} - 6.92 \cdot 10^{- 5} n^{2} + 32, 280.66 r + 0.0000010 w + 0.0610159 n + 0.1779493$
4	$y_{4} (r, w, n) = - 7.11 \cdot 10^{5} r^{2} - 3.82 \cdot 10^{- 5} w^{2} - 7.07 \cdot 10^{- 5} n^{2} + 38, 956.53 r + 0.0131744 w + 0.0432329 n + 2.6488897$

CROP	r * (%)	w * ( mm )	n * ( kg )	y_i ( w , n ) ( kg.ha ⁻¹)	iterations
1	0.020000	284.677897	99.997970	127.737290	22
2	0.072338	197.289649	99.980918	2,661.670057	18
3	0.023091	50.002803	99.999517	378.073711	24
4	0.027396	172.444253	99.997712	541.019584	21

CROP	r * (%)	w * ( mm )	n * ( kg )	y_i ( w , n ) ( kg.ha ⁻¹)	iterations
1	0.020000	284.677198	249.993749	130.263644	22
2	0.072338	197.294137	132.900164	2,661.734410	18
3	0.023091	150.001472	249.998638	381.963170	22
4	0.027396	172.463383	249.995135	543.792798	22

CROP	r * (%)	w * ( mm )	n * ( kg )	y_i ( w , n ) ( kg.ha ⁻¹)	iterations
1	0.020000	284.679514	199.996114	129.635030	22
2	0.072338	197.290397	132.896571	2,661.734410	18
3	0.023091	100.000656	199.999679	381.488126	23
4	0.027396	172.442217	199.998920	543.221925	22

PLANT	r * (%)	w * ( mm )	n * ( kg )	NI_i ( w , n ) (R$. ha ⁻¹)	iterations
1	0.020000	266.004924	0.000008	6,076.890235	82
2	0.072338	187.358504	0.000007	20,1637.752514	79
3	0.023091	50.000015	0.000008	25,206.891131	81
4	0.027396	150.344844	0.000008	37,896.874814	81

PLANT	r * (%)	w * ( mm )	n * ( kg )	NI_i ( w , n ) (R$. ha ⁻¹)	iterations
1	0.020000	283.598369	75.000001	4,018.559499	23
2	0.072338	196.714125	75.000001	190,435.879388	19
3	0.023091	150.000010	75.000001	22,267.758534	23
4	0.027396	171.162354	75.000001	34,406.058711	23

PLANT	r * (%)	w * ( mm )	n * ( kg )	NI_i ( w , n ) (R$. ha ⁻¹)	iterations
1	0.020000	261.803849	75.000001	2,121.380755	23
2	0.072338	185.124526	75.000001	143,875.052563	19
3	0.023091	100.000032	75.000001	16,073.656423	23
4	0.027396	145.374247	75.000003	25,239.492131	22

\begin{array}{l} maximize & y (r, w, n) = a r^{2} + b w^{2} + c n^{2} + f r + g w + h n + m \\ subject to & r_{i n f} \leq r \leq r_{s u p} \\ w_{i n f} \leq w \leq w_{s u p} \\ n_{i n f} \leq n \leq n_{s u p} \end{array}

\begin{array}{l} maximize & N I (r, w, n) = p_{c} y (r, w, n) - c_{w} w - c_{n} n - c_{0} \\ subject to & r_{i n f} \leq r \leq r_{s u p} \\ w_{i n f} \leq w \leq w_{s u p} \\ n_{i n f} \leq n \leq n_{s u p}, \end{array}

\begin{array}{l} maximize & N I (r, w, n) = a p_{c} r^{2} + b p_{c} w^{2} + c p_{c} n^{2} + f p_{c} r + (g p_{c} - c_{w}) w + (h p_{c} n - c_{n}) n + (p_{c} m - c_{0}) \\ subject to & r_{i n f} \leq r \leq r_{s u p} \\ w_{i n f} \leq w \leq w_{s u p} \\ n_{i n f} \leq n \leq n_{s u p} . \end{array}

[1] * Corresponding author. Universidade Federal Rural do Rio de Janeiro - UFRRJ/ Seropédica - RJ, Brasil. E-mail: vinicius.nascimento@ufrrj.br

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MAXIMIZATION OF PRODUCTION AND NET INCOME IN AGRO-FOREST SYSTEMS

ABSTRACT